# Mean-field analysis of synaptic alterations underlying deficient cortical gamma oscillations in schizophrenia

## TL;DR

This study explores how changes in brain cell connections may lead to reduced gamma brain waves in schizophrenia, using mathematical models to understand the underlying mechanisms.

## Contribution

The paper introduces a mean-field model to analyze how synaptic alterations synergistically disrupt gamma oscillations in schizophrenia.

## Key findings

- Lower strength of E→I and I→E synapses and greater E→I variability synergistically reduce gamma oscillations in a mean-field model.
- Bifurcation analyses reveal that reduced E→I synaptic strength primarily drives the disruption of gamma oscillations.
- The model predicts how multiple synaptic changes interact to robustly lower prefrontal cortex gamma power in schizophrenia.

## Abstract

Deficient gamma oscillations in the prefrontal cortex (PFC) of individuals with schizophrenia (SZ) are proposed to arise from alterations in the excitatory drive to fast-spiking interneurons (E→I) and in the inhibitory drive from these interneurons to excitatory neurons (I→E). Consistent with this idea, prior postmortem studies showed lower levels of molecular and structural markers for the strength of E→I and I→E synapses and also greater variability in E→I synaptic strength in PFC of SZ. Moreover, simulating these alterations in a network of quadratic integrate-and-fire (QIF) neurons revealed a synergistic effect of their interactions on reducing gamma power. In this study, we aimed to investigate the dynamical nature of this synergistic interaction at macroscopic level by deriving a mean-field description of the QIF model network that consists of all-to-all connected excitatory neurons and fast-spiking interneurons. Through a series of numerical simulations and bifurcation analyses, findings from our mean-field model showed that the macroscopic dynamics of gamma oscillations are synergistically disrupted by the interactions among lower strength of E→I and I→E synapses and greater variability in E→I synaptic strength. Furthermore, the two-dimensional bifurcation analyses showed that this synergistic interaction is primarily driven by the shift in Hopf bifurcation due to lower E→I synaptic strength. Together, these simulations predict the nature of dynamical mechanisms by which multiple synaptic alterations interact to robustly reduce PFC gamma power in SZ, and highlight the utility of mean-field model to study macroscopic neural dynamics and their alterations in the illness.